Method of forming a graphene structure

ABSTRACT

In various embodiments, a method of forming a graphene structure is provided. The method may include forming a body including at least one protrusion, and forming a graphene layer at an outer peripheral surface of the at least one protrusion.

RELATED APPLICATION(S)

This application is a divisional of U.S. patent application Ser. No.14/587,007, filed on Dec. 31, 2014, entitled “METHOD OF FORMING AGRAPHENE STRUCTURE”, which is incorporated herein by reference in itsentirety.

TECHNICAL FIELD

Various embodiments relate generally to a method of forming a graphenestructure.

BACKGROUND

Carbon nanotubes may have advantageous properties, for example regardingtheir electrical or thermal conductivity, or regarding their hardness,e.g. a mechanical hardness. At present, carbon nanotubes are formed in away that may make it difficult to form carbon nanotubes with a definedlength and/or with a defined diameter. Furthermore, a shape of thecarbon nanotubes may be restricted to circular hollow cylinders.

SUMMARY

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming a body including at least oneprotrusion. The method may further include forming a graphene layer atan outer peripheral surface of the at least one protrusion.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. The drawings are not necessarilyto scale, emphasis instead generally being placed upon illustrating theprinciples of the invention. In the following description, variousembodiments of the invention are described with reference to thefollowing drawings, in which:

FIGS. 1A to 1E show various stages of a method of forming a graphenestructure in accordance with various embodiments;

FIGS. 2A and 2B show two stages of a method of forming a graphenestructure according to various embodiments;

FIGS. 3A and 3B show graphene structures in accordance with variousembodiments;

FIGS. 4A to 4F show various stages of a method of forming a transistorin accordance with various embodiments;

FIGS. 5A to 5C show various stages of a method of forming a graphenestructure in accordance with various embodiments;

FIGS. 6A and 6B show various stages of a method of forming a graphenestructure in accordance with various embodiments;

FIG. 7 shows a schematic diagram of a method of forming a graphenestructure in accordance with various embodiments;

FIG. 8 shows a schematic diagram of a method of forming a graphenestructure in accordance with various embodiments; and

FIG. 9 shows a schematic diagram of a method of forming a graphenestructure in accordance with various embodiments.

DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and embodiments inwhich the invention may be practiced.

Various aspects of the disclosure are provided for devices, and variousaspects of the disclosure are provided for methods. It will beunderstood that basic properties of the devices also hold for themethods and vice versa. Therefore, for sake of brevity, duplicatedescription of such properties may have been omitted.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration”. Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

The word “over” used with regards to a deposited material formed “over”a side or surface, may be used herein to mean that the depositedmaterial may be formed “directly on”, e.g. in direct contact with, theimplied side or surface. The word “over” used with regards to adeposited material formed “over” a side or surface, may be used hereinto mean that the deposited material may be formed “indirectly on” theimplied side or surface with one or more additional layers beingarranged between the implied side or surface and the deposited material.

The words “cylinder”, “cylindrical” and the like are to be understood asreferring to a surface traced by a straight line moving parallel to afixed straight line and intersecting a fixed planar closed curve. Inother words, a cylinder may not only include three-dimensionalstructures with a circular or elliptical cross section, but also withcross sections an outline of which is of any other regular or irregularshape, e.g. a polygon (e.g. a triangle, rectangle, square, hexagon,etc.), a half-moon shape, etc., as long as the outline of the crosssection (the curve in the fixed plane) is closed.

The term “at least one graphene layer” as used herein means at least one1-atom thick layer of carbon atoms and thus includes a single-atom thicklayer of carbon atoms and a multi-atom thick layer of carbon atoms suchas a 2-atoms thick layer, a 3-atoms thick layer, a 4-atoms thick layer,a 5-atoms thick layer, a 6-atoms thick layer of carbon atoms, forexample.

In the following, a graphene layer and a graphene structure may bereferred to. The (e.g. at least one) graphene layer may be considered asforming a very thin, e.g. only up to a few atoms (see above) thicklayer, i.e. to be formed extending in two layer dimensions and to have anegligible extent in a third dimension. The graphene layer may howeverbe arranged also in a third dimension, it may for example be bent and/orlinked in the third dimension, thereby forming a three-dimensionalgraphene structure. The graphene layer may thus be considered as beingshaped in the third dimension to form the graphene structure, and thegraphene structure may be considered as a three-dimensional arrangementof the essentially two-dimensional graphene layer.

In various embodiments, a method of forming carbon nanotubes in adefined way may be provided.

The carbon nanotubes formed using a method according to variousembodiments may for example be used for forming switchable (e.g.electronic) devices, e.g. transistors.

In various embodiments, a protrusion may be formed on or from acarbon-containing semiconductor body. At a surface of the protrusion, agraphene layer may be formed.

In various embodiments, a carbon-containing semiconductor (e.g. SiC)substrate may be structured, e.g. by forming trenches in the substrate,in such a way that one or more protrusions, e.g. pillar- and/ormesa-shaped structures (which may be referred to as mesa structures),e.g. SiC mesa structures, may be formed. Subsequently, the structuredsubstrate may be annealed, such that a surface of the at least one mesastructure may be converted to a graphene layer.

In other words, a carbon-containing (e.g. SiC) substrate may be used forforming a protrusion. The substrate with the protrusion may be subjectedto an annealing process, which may lead to a formation of a graphenelayer on an exposed surface of the protrusion. The graphene layer mayform by thermal decomposition of the substrate material (e.g., siliconcarbide). This process for forming the graphene layer may also bereferred to as epitaxy, expitaxial formation or epitaxial growth of thegraphene layer, even though the carbon used for forming the graphenelayer may be provided by the carbon-containing semiconductor materialitself and not deposited in a deposition process that may typically bereferred to as epitaxial deposition, epitaxy, expitaxial formation orepitaxial growth.

In one or more embodiments, a very precise structurability ofsemiconductor substrates, for example using extreme ultraviolet- orelectron beam lithography, may be exploited for forming a graphenestructure with a precisely pre-defined shape. First, a precisely shapedprotrusion may be formed from and/or on a carbon-containing substrate,e.g. an SiC substrate, and thereafter the graphene structure may beformed at or on an outer surface of the precisely shaped protrusion,thereby creating a precisely shaped graphene structure. An annealingprocess may be used for the forming of the graphene structure.

In various embodiments, a method of forming carbon nanotubes in awell-defined way may be provided. The carbon nanotubes may be formed byforming at least one graphene layer surrounding, e.g. wrapping, asilicon carbide mesa structure, e.g. a pillar shaped silicon carbidemesa structure. The carbon nanotubes may, in various embodiments, befilled with silicon carbide, which may be remaining SiC material of themesa structure(s). Alternatively, the silicon carbide may be removedfrom an inside of the carbon nanotubes.

In various embodiments, a plurality of pillars containing siliconcarbide may be formed. From the plurality of pillars, a plurality ofcarbon nanotubes may be formed by thermal decomposition of the siliconcarbide at an outer peripheral surface of the plurality of pillars.

In various embodiments, a graphene structure may be formed bypre-shaping a body to have a peripheral surface with a shape (e.g. acylindrical shape) desired for the graphene structure, and by forming agraphene layer on the peripheral surface. In the following, variousembodiments may be described in detail with reference to the figures.

In the embodiments, the graphene layer may be formed on an outerperipheral surface (e.g. of a protrusion). Alternatively, the graphenelayer may be formed on an inner peripheral surface (e.g. of an openingformed in a body), and a portion of the body outside the graphene layer(which may form a closed surface) may be removed, or the graphene layermay be formed on an inner peripheral surface of an opening formed in abody, wherein the opening may have such a specific diameter that acarbon nanotube may form, in other words, the diameter of the openingmay fulfill a specific relation.

In the embodiments, the body, or at least a peripheral surface of theprotrusion, may be described as including or consisting ofcarbon-containing semiconductor material. Alternatively, the body, or atleast a peripheral surface of the protrusion and/or the opening, may forexample be a metal with carbon dissolved in its bulk above itsdissolution limit (the carbon may for example be introduced bycodeposition or by solution from a carbon-containing gas at elevatedtemperatures). After an annealing/cooling sequence, graphene may beformed by carbon segregation to the metal surface. And in yet anotheralternative, the peripheral surface of the protrusion and/or the openingmay be catalytic, e.g. include or consist of copper (Cu), nickel (Ni) orgermanium (Ge), and graphene may be deposited on the catalytic surfaceby chemical vapor deposition from a carbon-containing gas. All thesematerials may be wet chemically etched selectively to graphene. Graphenedeposition using metals may yield polycrystalline graphene. Germaniummay easily be etched anisotropically. CVD on single-crystallinegermanium (Ge) may yield single-crystalline graphene. As a consequence,unless specifically excluded and/or unfeasible, the various embodimentsdescribed below may be carried out by applying one or more of the abovedescribed modifications.

FIGS. 1A to 1C show various stages of a method of forming a graphenestructure in accordance with various embodiments.

As shown in FIG. 1A, a semiconductor body 102 may be provided. Thesemiconductor body 102 may have a first surface 1021 on a first side,also referred to as a top surface and a top side, respectively, and asecond surface 1022 on a second side, also referred to as a bottomsurface and a bottom side, respectively, opposite the first surface 1021(and opposite the first side).

In various embodiments, the semiconductor body 102 may include carbon.The semiconductor body 102 may include, consist of or essentiallyconsist of a semiconductor material including carbon. The semiconductormaterial including carbon may be referred to as a carbon-containingsemiconductor material. The semiconductor body 102 may for exampleinclude, consist of or essentially consist of silicon carbide (SiC).Alternatively, the semiconductor body 102 may for example include,consist of or essentially consist of germanium carbide (GeC). In variousembodiments, the semiconductor body 102 may be a semiconductorsubstrate, e.g. a semiconductor wafer, e.g. a silicon carbide wafer. Invarious embodiments, the semiconductor body 102 may include at least onematerial that may not be a semiconductor material, or a semiconductormaterial that may not contain carbon. For example, a layer of thecarbon-containing semiconductor material may be formed on a carrier(which may or may not include a semiconductor material and may or maynot include carbon). In that case, a body formed from the carrier andthe layer of the carbon-containing semiconductor material may beconsidered as the semiconductor body 102.

In various embodiments, the semiconductor body 102 may at leastpartially be doped. The semiconductor body 102 may for example be, e.g.partially, doped as a p-type semiconductor and/or as an n-typesemiconductor. In various embodiments, the semiconductor body 102 mayinclude an epitaxial layer of the semiconductor material.

On a surface of the semiconductor body 102, e.g. on the first surface1021 of the semiconductor body 102, a masking structure 104 may bearranged. The masking structure 104 may include any material that issuitable for protecting the semiconductor body 102 underneath themasking structure 104 from being removed during a subsequent structuringprocess. The masking structure 104 may for example include or consist ofa hard mask, a photoresist or a resist used in electron beamlithography.

In various embodiments, the masking structure 104 may be formed having atwo-dimensional structure (e.g. a two-dimensional distribution on thefirst surface 1021 of the semiconductor body 102) corresponding to across section of one or more protrusions 106 (see FIG. 1B) to be formedfrom the semiconductor body 102. A patterning of the masking structuremay for example include extreme ultraviolet- or electron beamlithography.

The semiconductor body 102 may in various embodiments be subjected to astructuring process, leading to a structured semiconductor body 102including a semiconductor base 102 b (also referred to as semiconductorbase region 102 b) and the at least one protrusion 106, for example asshown in FIG. 1B.

The structuring process may include etching (e.g. wet etching or dryetching), for example at least one of photoelectrochemical wet etchingin hydrogen fluoride (HF, e.g. 2.5 molar) combined with UV irradiation(which may lead to an isotropic etching), plasma etching using sulfurhexafluoride with oxygen plasma (SF₆/O₂ plasma, which gives thepossibility to adjust etching characteristics from isotropic toanisotropic), plasma etching using trifluoromethane with oxygen plasma(CHF₃/O₂ plasma, which may lead to an anisotropic etching), and plasmaetching using tetrafluoromethane with oxygen plasma (CF₄/O₂ plasma,which may lead to an anisotropic etching), or etching with potassiumhydroxide solution. The material of the masking structure 104 may bechosen to match the etchant to be used, in the sense that the maskingstructure 104 may essentially resist the etchant, e.g. it may not beremoved or may be removed much slower than the carbon-containingsemiconductor material of the semiconductor body 102 during the etchprocess.

In other words, using a structuring process, for example using anetching process, for example using one of the etchants described above,the semiconductor body 102 may be structured, wherein the maskingstructure 104 may serve as a mask, masking one or more regions of thesemiconductor body that are not supposed to be (at least partially)removed during the structuring process. Thereby, the semiconductor body102 may be formed, e.g. structured, in such a way that it includes atleast one protrusion 106 including the carbon-containing semiconductormaterial. Furthermore, the semiconductor body may include thesemiconductor base (or base region) 102 b.

After the structuring, the masking structure 104 may in variousembodiments be removed, as shown in FIG. 1B. Thereby, thecarbon-containing semiconductor material of the semiconductor body 102may be exposed at the top surface 1021.

Alternatively, the masking structure 104 may remain, for example toprevent a formation of a graphene layer in the masked regions of thesemiconductor body 102. In other words, in regions where the maskingstructure 104 may be left on the carbon-containing semiconductormaterial of the semiconductor body 102, e.g. on a top of the at leastone protrusion 106, the carbon-containing semiconductor material may notbe exposed, such that a subsequent annealing process may not lead to aformation of a graphene layer in the masked regions of the semiconductorbody 102.

In various embodiments, the at least one protrusion 106 of thesemiconductor body 102 may be formed by epitaxial growth ofcarbon-containing semiconductor material on the semiconductor body 102,which may be regarded as the semiconductor base 102 b, e.g. on the firstsurface 1021, or by a combination of epitaxial growth and removal (e.g.etching) of the carbon-containing semiconductor material. The at leastone protrusion 106 formed by epitaxial growth or by a combination ofepitaxial growth and removal may be considered as forming a part of thesemiconductor body 102.

After a formation of the at least one protrusion 106, a portion of asurface of the semiconductor body 102 from which the at least oneprotrusion 106 extends (and which may be opposite the second surface1022 of the semiconductor body 102), i.e. a portion of a surface of thesemiconductor base 102 b, may be referred to as a first recessed surface1021 r of the semiconductor body 102, irrespective of whether the atleast one protrusion 106 was formed by building it on the first surface1021 of the semiconductor body 102 (e.g. by epitaxial growth), such thatthe first recessed surface 1021 r corresponds to at least a portion ofthe first surface 1021, or whether the at least one protrusion 106 wasformed by removing the semiconductor material around it, thereby newlycreating the first recessed surface 1021 r.

In various embodiments, the at least one protrusion 106 may be formed insuch a way that it extends away from the first recessed surface 1021 rof the semiconductor body 102. A first end 1061 of the at least oneprotrusion 106 may be connected to, e.g. integrally formed with, thesemiconductor base 102 b of the semiconductor. A second end 1062 of theprotrusion 106 may be opposite the first end 1061 of the protrusion 106.

The at least one protrusion 106 may have a length 106L, wherein thelength 106L of the at least one protrusion 106 may be measured betweenthe first end 1061 of the protrusion and the second end 1062 of theprotrusion 106, for example along a central axis (also referred to asthe long axis) of the at least one protrusion 106. The length of theprotrusion 106 may correspond to a height of a top, e.g. a top of thesecond end 1062, of the protrusion 106, above the first recessed surface1021 r. The length 106L of the protrusion 106 may be in a range fromabout 1 nm to about 1 mm, for example from about 20 nm to about 500 nm,for example from about 50 nm to about 200 nm, although other values ofthe length may be possible as well.

A width 106W of the at least one protrusion 106 may be measured in adirection essentially orthogonal to the length 106L of the protrusion106. In FIG. 1B, this may correspond to a horizontal direction. If, invarious embodiments, the at least one protrusion 106 may be circularlycylindrical, the width 106W may be the same in all directions in whichthe width 106W of the at least one protrusion 106 may be measured. Inthis case, the width 106W may correspond to a diameter of the circularlycylindrical protrusion 106. In various other embodiments, the width ofthe protrusion 106 may be different for at least some of the(horizontal) directions, in which the width 106W of the at least oneprotrusion 106 may be measured, for example in a case where a crosssection of the at least one protrusion 106 is rectangular, elliptical,or of some other polygonal or irregular shape. In that case, ifrelevant, several values may be specified for the width 106W of theprotrusion 106, e.g. a minimum and a maximum width, etc.

In various embodiments, the width 106W of the at least one protrusion106 may be essentially constant along the length 106L of the protrusion106. Alternatively, the width 106W of the at least one protrusion 106may vary along the length 106L of the protrusion. For example, the atleast one protrusion 106 may have a larger width 106W near the first end1061 of the protrusion 106 than near the second end 1062 of theprotrusion 106, or vice versa.

In various embodiments, the width 106W of the at least one protrusion106 may be greater than or equal to about 0.4 mm, for example in a rangefrom about 0.4 nm (which may correspond to a minimum diameter of acarbon nanotube) to about 200 nm, for example from about 1 nm to about20 nm, for example from about 5 nm to about 10 nm.

In various embodiments, the at least one protrusion 106 may have acylindrical shape. In other words, an outer peripheral surface 106 o ofthe protrusion 106 may be cylindrical. The cross section of the at leastone protrusion 106 may have an outline that is of any other regular orirregular closed shape, e.g. a circle, an ellipse, a polygon (e.g. asquare, a rectangle, a hexagon, a trapezium or the like), a half-moonshape, etc. An exemplary cross section along a line A-A′ of a circularlycylindrical protrusion 106 (i.e. the cross section shows the outerperipheral surface 106 o being circular) is shown in view 100A of FIG.1B. In various embodiments, the cylinder may be a straight cylinder. Inother words, the at least one cylindrical protrusion 106 may be arrangedsuch that its long axis is essentially orthogonal to the first recessedsurface 1021 r and/or to the second surface 1022 of the semiconductorbody 102. In various other embodiments, the at least one protrusion 106may be arranged such that its long axis is inclined with respect to thefirst recessed surface 1021 r and/or to the second surface 1022 of thesemiconductor body 102.

In various embodiments, the protrusion 106 may have any other regular orirregular shape, for example a pyramid, a cone, a frustum, or a randomlyshaped protrusion 106.

In various embodiments, a crystal structure of the carbon-containingsemiconductor material may be taken into account for the forming of theat least one protrusion 106 in order to form a desired surfaceconfiguration of the outer surface 106 o of the at least one protrusion106. For example, the semiconductor body 102 with the at least oneprotrusion 106 may be formed in such a way that a pre-defined portion ofthe outer surface 106 o of the protrusion 106 coincides with apre-defined crystal plane of the carbon-containing semiconductormaterial. Thereby, for example, a termination of the semiconductormaterial at the pre-defined portion of the outer surface 106 o of theprotrusion 106 may be defined. In a case of a silicon carbidesemiconductor material, a crystal cut along a (0001) plane of thesilicon carbide may lead to two differently terminated surfaces, alsoreferred to as faces: on one side of the cut, a carbon-terminatedsurface (also referred to as C-face) may form, while on another side ofthe cut, a silicon-terminated surface (also referred to as Si-face) mayform. The surface termination along the outer surface 106 o of the atleast one protrusion 106 may have an impact on properties of a graphenelayer to be formed, as described below.

In order to take into account the crystal structure of thecarbon-containing semiconductor material, a relative orientation of thesemiconductor body 102 and the at least one protrusion 106 to be formedmay be chosen such that the pre-defined portion of the outer surface 106o of the protrusion 106 may coincide with a pre-defined face of a cutthrough the crystal of the semiconductor material, for example along thepre-defined crystal plane. For example, the at least one protrusion 106may have a rectangular cuboid shape, in other words, the outer surface106 o of the protrusion may 106 have two pairs of opposite equal facesthat are at right angles to each other, the carbon-containingsemiconductor material may be silicon carbide, and the relativeorientation of the silicon carbide and the at least one protrusion 106may be such that one of the faces of the outer surface 106 o of theprotrusion 106 may be a C-face, and the opposite face of the protrusion106 may be an Si-face, for example a plane of the C-face and/or of theSi-face may be essentially or exactly parallel to the (0001) plane ofthe silicon carbide. In various other embodiments, other shapes of theat least one protrusion 106, other relative orientation and/or othersemiconductor material may be used for obtaining a desired surfaceconfiguration of the outer surface 106 o of the at least one protrusion106.

In various embodiments, like in the exemplary embodiment of therectangular cuboid protrusion 106 with the C-face and the Si-face, thesurface configuration of the outer surface 106 o of the at least oneprotrusion 106 may vary along an azimuthal direction of the outersurface 106 o of the protrusion. For example, in a first azimuthaldirection of the at least one protrusion 106, a first surfaceconfiguration (for example a C-face) may be encountered on the outersurface 106 o, in a second azimuthal direction of the at least oneprotrusion 106, a second surface configuration (for example an Si-face,for example if the two azimuthal directions differ by about 180°) may beencountered, and one or more further surface configurations (for examplea mixed face, with silicon and carbon alternating) may be encountered inone or more further azimuthal directions.

In a case where a plurality of protrusions 106 is formed, the pluralityof protrusions 106 may in various embodiments be essentially identicalto each other, i.e. each of the protrusions 106 may have essentially thesame length, essentially the same width, and essentially the same shape.Furthermore, a basic arrangement of the plurality of protrusions 106 maybe the same, e.g. they may all be arranged with their long axes pointingin the same direction, and/or in a case where the width 106W variesalong the length 106L of the protrusions 106, all the protrusions 106may be arranged with the wider end at the same position, e.g. with thewider end being connected to the semiconductor base 102 b and thenarrower end pointing away from the semiconductor base 102 b, or viceversa.

In various embodiments, properties of the individual protrusions 106 ofthe plurality of protrusions 106 and/or their arrangement on thesemiconductor base 102 b may vary, e.g. be inhomogeneous. For example,the length 106L, the width 106W, and/or the shape of the individualprotrusions 106 may be different. Furthermore, the long axes of theindividual protrusions 106 may point to different directions.

In various embodiments, the plurality of protrusions 106 may bearranged, for example on the semiconductor base 102 b of thesemiconductor body 102, with a separation 106S between each adjacentpair of protrusions 106. The separation 106S may refer to a distancebetween the outer surfaces 106 o of two adjacent protrusions 106.

In various embodiments, the separation 106S between each pair ofadjacent protrusions 106 may be greater than or equal to about 1 nm, forexample in a range from about 1 nm to about 1 cm, e.g. between about 5nm and about 1 μm.

In various embodiments, the plurality of protrusions 106 may be arrangedto form a regular pattern. In other words, the plurality of protrusions106 may be arranged having a recurrent structure (e.g. distribution ofpositions of the protrusions 106 and/or of the separations 106S betweenthem). For example, the protrusions 106 may be arranged forming aregular grid, for example, in a case where the plurality of protrusions106 may be formed from a semiconductor wafer 102, the plurality ofprotrusions 106 may be arranged such that one or more of the protrusions106 are formed in an essentially identical fashion on each of aplurality of chips to be formed from the semiconductor wafer 102.

In various embodiments, the plurality of protrusions may be arrangedirregularly or only partially structured. For example, the positions ofthe protrusions 106, e.g. on the semiconductor base 102 b, and/or theseparations 106S between the protrusions 106, may vary irregularly, e.g.randomly.

Describing the process shown in FIG. 1A and FIG. 1B in other words,various embodiments of a method of forming a graphene structure mayinclude forming at least one semiconductor structure 106 having acylindrical surface 106 o, the at least one semiconductor structure 106projecting from at least one surface 1021 r of a semiconductor substrate102 and including carbon-containing semiconductor material.

In various embodiments, as shown in FIG. 1C, a graphene layer 108 may beformed at least at a peripheral portion of the outer surface 106 o ofthe at least one protrusion 106. In other words, a process of forming agraphene layer 108 at an outer peripheral surface of the at least oneprotrusion 106 may be executed. An outer surface of the graphene layer108 may be uncovered.

The process of forming the graphene layer 108 may, in variousembodiments, include an annealing process. The semiconductor body 102may be heated to an elevated temperature, which may also be referred toas an annealing temperature. The elevated temperature may be in a rangefrom about 1150° C. to about 1800° C. In various embodiments, theelevated temperature during the forming of the graphene layer may be ina range from about 1150° C. to about 1400° C., for example from about1150° C. to about 1350° C., for example from about 1200° C. to about1300° C., e.g. if the forming of the graphene layer is executed invacuum, e.g. at a pressure at about 10⁻⁸ mbar or lower, e.g. inultra-high vacuum. In various embodiments, the elevated temperatureduring the forming of the graphene layer may be in a range from about1550° C. to about 1800° C., for example from about 1600° C. to about1700° C., for example about 1650° C., e.g. if the forming of thegraphene layer 108 is executed at approximately atmospheric pressure,e.g. at a pressure from about 800 mbar to about 1000 mbar, e.g. about900 mbar, for example in an atmosphere including, consisting of oressentially consisting of argon.

The semiconductor body 102 may be kept at the elevated temperature for atime referred to as the heating duration or as the annealing duration,respectively. The heating duration may, in various embodiments, be in arange from about 5 minutes to about 60 minutes, for example from about10 minutes to about 30 minutes, for example about 15 minutes.

In various embodiments, a subsequent annealing process of heating thesemiconductor body 102 to a temperature in a range from about 600° C. toabout 1000° C., for example in an atmosphere including, consisting of oressentially consisting of hydrogen, may decouple a semiconductorbody-graphene interaction for example by saturating dangling bonds at aresulting surface of SiC forming underneath the graphene layer 108. Invarious embodiments, different intercalation materials may be used, e.g.Ge, Si, which may be advantageous for a subsequent etching process.

The at least one graphene layer 108 may be formed by thermaldecomposition of the carbon-containing semiconductor material of thesemiconductor body 102, e.g. silicon carbide, at a surface, e.g. anexposed surface, of the semiconductor body 102. In other words, in oneor more regions where the carbon-containing semiconductor material ofthe semiconductor body 102 may be exposed, e.g. exposed to vacuum or toan atmosphere, during the annealing process, the at least one graphenelayer 108 may form by thermal decomposition of the carbon-containingsemiconductor material. During the annealing process, atoms of thecarbon-containing semiconductor material except the carbon, e.g. siliconatoms of silicon carbide, may sublime if the carbon-containingsemiconductor material is exposed to vacuum or to an atmosphere, leavingbehind excess carbon at the surface of the carbon-containingsemiconductor material. The excess carbon may bond to form graphene,e.g. at least one graphene layer. The exposed surface formed by thecarbon-containing material of the semiconductor body 102 may at leastinclude the peripheral surface of the at least one protrusion 106 of thesemiconductor body 102. In other words, the at least one graphene layer108 may at least form at or on the peripheral surface of the at leastone protrusion 106. In various embodiments, other portions of thesurface of the semiconductor body 102 may be formed from thecarbon-containing semiconductor material and may be exposed, such thatthe at least one graphene layer 108 may also form in said portions ofthe surface of the semiconductor body 102, e.g. during the annealingprocess.

In the exemplary embodiment shown in FIG. 1C, the at least one graphenelayer 108 is also formed at or on the first recessed surface 1021 r andon a top surface, i.e. the surface at the second end 1062, of the atleast one protrusion 106. A formation of the at least one graphene layer108 at or on the second surface 1022 of the semiconductor body 102 andat or on the surface connecting the second surface 1022 with the firstrecessed surface 1021 r may be avoided by preventing an exposure ofthose surfaces, e.g. by covering those surfaces with a protecting layerand/or with a mechanical cover, e.g. a holding structure or a lid, insome embodiments.

In general, in various embodiments, portions of the surface of thesemiconductor body 102 at which, in addition to the outer peripheralsurface 106 o of the at least one protrusion 106, a forming of the atleast one graphene layer 108 may be desired may be formed from acarbon-containing semiconductor material and may be left exposed.Forming (and leaving in place) the graphene layer 108, completely or atleast partially, e.g. locally, also at portions of the surface of thesemiconductor body 102 other than the outer peripheral surface 106 o (asfor example shown in FIG. 1C and FIG. 1D) may for example be desired forforming an electrically conductive connection between a plurality ofgraphene layers 108, e.g. graphene structures 108 s, formed in differentregions of the semiconductor body 102. The plurality of graphene layers108, for example a plurality of carbon nanotubes 108 c, may beelectrically connected by the portion of the graphene layer 108 formedat or on the surface of the semiconductor body 102 between the carbonnanotubes 108 c, for example at or on the first recessed surface 1021 r,which may correspond to a bottom of a trench formed in the semiconductorbody 102 for forming the plurality of protrusions 106, or at or on adedicated additional structure, for example a connecting wall (notshown), e.g. a thin, vertical plate-like structure, formed between theplurality of protrusions 106.

Portions of the surface of the semiconductor body 102 at which a formingof the at least one graphene layer may not be desired may be covered,e.g. by a protective layer, a mechanical cover or the like, or they maybe formed from a material other than a carbon-containing semiconductormaterial.

In various embodiments, the at least one graphene layer 108 may beformed by epitaxially growing, e.g. depositing, the at least onegraphene layer at least on the outer peripheral surface 106 o of the atleast one protrusion 106. In various embodiments, portions of thesurface of the semiconductor body 102 at which, in addition to the outerperipheral surface 106 o of the at least one protrusion 106, a formingof the at least one graphene layer may be desired, may be formed from acarbon-containing semiconductor material and may be left exposed.Portions of the surface of the semiconductor body 102 at which a formingof the at least one graphene layer by deposition may not be desired maybe treated in such a way that either carbon is not deposited there forthe formation of the at least one graphene layer 108, or that thedeposited carbon, which may or may not have formed graphene, may easilybe removed, e.g. together with a protective layer formed in that region.

In various embodiments, the at least one graphene layer 108 may includea single atomic layer of graphene, also referred to as a single graphenelayer or graphene monolayer. Alternatively, the at least one graphenelayer 108 may include a graphene layer 108 having a thickness of morethan one atom, also referred to as graphene multilayer. For example, thegraphene layer 108 may be a 2-atoms thick layer, a 3-atoms thick layer,etc., up to approximately a 10-atoms thick layer.

In various embodiments, a pre-defined termination of thecarbon-containing semiconductor material, e.g., silicon carbide, atleast on the peripheral outer surface of the at least one protrusion106, e.g. as described above, e.g. the C-face, the Si-face and/or amixed face, may be used for pre-defining the thickness of the at leastone graphene layer 108. For example, on the C-face a thicker graphenelayer 108 may form than on the Si-face under the same processingconditions. For example, a 2-atoms thick layer may form on the C-face,wherein a 1-atom-thick layer may form on the Si-face.

In other words, a deliberately selected termination of the peripheralouter surface 106 o of the at least one protrusion 106 may represent aparameter of one or more parameters that may be adjusted in the methodof forming a graphene structure for obtaining the graphene structure 108s with desired properties.

In various embodiments, by creating the at least one graphene layer 108with a pre-defined thickness, for example by adjusting the properties ofthe carbon-containing semiconductor material and/or of processparameters of the process or processes carried out for the forming ofthe at least one graphene layer 108, properties of the at least onegraphene layer 108, e.g. a band gap and/or an electrical conductivity,of the at least one graphene layer 108 may be adjusted. In variousembodiments, e.g. in an example where the graphene layer 108 may formgraphene nanoribbons (e.g., having a width of less than or equal toabout 100 nm), in an example where the graphene layer 108 may be bent,or in an example where the graphene layer 108 may be a 2-atoms thicklayer, or, more generally, thicker than a monolayer, a band gap mayform.

In various embodiments, the process parameters that may be adjusted foradjusting the properties of the graphene layer 108 may include theannealing temperature. For example, annealing the semiconductor body 102at a comparatively high temperature, e.g. with a temperature in a rangefrom about 1550° C. to about 1800° C., for example from about 1600° C.to about 1700° C., for example about 1650° C., may lead to a formationof predominantly or exclusively graphene monolayers. In that case, theannealing may be executed at approximately atmospheric pressure, e.g. ata pressure from about 800 mbar to about 1000 mbar, e.g. about 900 mbar,for example in an atmosphere including, consisting of or essentiallyconsisting of argon. For example, annealing the semiconductor body 102at a comparatively low temperature, e.g. with a temperature in a rangefrom about 1150° C. to about 1400° C., for example from about 1150° C.to about 1350° C., for example from about 1200° C. to about 1300° C.,may lead to a formation of predominantly graphene multilayers. In thatcase, the annealing may be executed in vacuum, e.g. at a pressure atabout 10⁻⁸ mbar or lower, e.g. in ultra-high vacuum. Varying theannealing temperature within the given range may allow adjusting thenumber of atomic layers the graphene layer 108 may include. Annealingthe semiconductor body 102 at an annealing temperature in a range fromabout 1150° C. to about 1250° C. may for example result in a graphenelayer 108 with fewer atomic layers than annealing the semiconductor body102 at an annealing temperature in a range from about 1250° C. to about1400° C.

The semiconductor body 102 may be kept at the elevated temperature for atime referred to as the heating duration or annealing duration. Theheating duration may, in various embodiments, be in a range from about 5minutes to about 60 minutes, for example from about 10 minutes to about30 minutes, for example about 15 minutes.

In various embodiments, the process parameters that may be adjusted foradjusting the properties of the graphene layer 108 may include theannealing duration. For example, annealing the semiconductor body 102for a comparatively long time, e.g. with an annealing duration in arange from about 30 minutes to about 60 minutes may lead to a thickergraphene layer 108, e.g. to a graphene multilayer, e.g. a graphenemultilayer with more atomic layers than achieved with a shorterannealing duration, for example in a range from about 5 minutes to about30 minutes.

In various embodiments, the thickness of the at least one graphene layer108 formed at or on the outer peripheral surface 106 o of the at leastone protrusion 106 may vary for different portions of the graphene layer108. For example, a first portion of the at least one graphene layer 108formed in a first azimuthal direction of the at least one protrusion 106or on a first face of the at least one protrusion 106 may have adifferent thickness than a second portion of the at least one graphenelayer 108 formed in a second azimuthal direction of the at least oneprotrusion 106 or on a second face of the at least one protrusion 106.For example, on an Si-face of the at least one protrusion 106, a singlegraphene layer 108 may form, whereas on an opposite C-face of the atleast one protrusion 106, a graphene multilayer 108 may form. The atleast one graphene layer 108 may, in various embodiments, thus beconsidered as being faceted.

In various embodiments, a faceting of the at least one graphene layer108 may, alternatively or additionally, concern other properties of theat least one graphene layer 108, e.g. an electrical and/or thermalconductivity and/or a structure in which the carbon atoms of the atleast one graphene layer are bonded. For example, the carbon atoms may,in a first azimuthal direction of the at least one protrusion 106, bebonded in a way that may resemble a so-called armchair configuration ofa carbon nanotube, and may, in a second azimuthal direction, be bondedin a way that may resemble a so-called zigzag- or a so-called chiralconfiguration of a carbon nanotube.

In various embodiments, the at least one graphene layer 108 may form athree-dimensional graphene structure 108 s. A shape, e.g. athree-dimensional shape of the at least one graphene layer 108, e.g. awidth, length and a way in which the two-dimensional graphene layer 108may be arranged, e.g. bent and/or linked, in a third dimension, may bepre-defined by the outer peripheral surface 106 o of the at least oneprotrusion 106. In other words, since the at least one graphene layer108 may be formed at the outer peripheral surface 106 o of the at leastone protrusion 106, e.g. using carbon atoms provided by thecarbon-containing semiconductor material forming the at least oneprotrusion 106 (and thus the outer peripheral surface 106 o of the atleast one protrusion 106) or by being deposited on the outer peripheralsurface 106 o of the at least one protrusion 106, the graphene layer 108may assume the shape pre-defined by the outer peripheral surface 106 oof the at least one protrusion 106. The length of the graphene structure108 s, e.g. a carbon nanotube 108 c, which may be measured in the samedirection as the length 106L of the at least one protrusion 106, may bedefined by the length 106L of the at least one protrusion 106, forexample by a height of pillars, mesa-like structures, circular cylindersor the like above the first recessed surface 1021 r. A width, e.g. adiameter, e.g. an inner diameter, of the graphene structure 108 s may bedefined by the width 106W, e.g. the diameter d, e.g. an outer diameterd, of the at least one protrusion 106, e.g. the pillars, mesa-likestructures, circular cylinders or the like.

In various embodiments, the annealing of the semiconductor body 102,e.g. of a semiconductor substrate 102, may lead to a forming of grapheneat the outer surface, e.g. the outer peripheral surface 106 o, e.g. thecylindrical surface, of the at least one protrusion 106, e.g. asemiconductor structure, e.g. a semiconductor structure formed fromcarbon-containing semiconductor material, thereby forming at least onecylindrical graphene structure 108 s.

In various embodiments, for example in a case where the outer peripheralsurface 106 o of the at least one protrusion 106 may be cylindrical,e.g. circularly cylindrical or polygonal, the at least one graphenelayer 108 may form at least one carbon nanotube 108 c.

In various embodiments, the at least one protrusion 106 may be formedwith a shape and/or a dimension (e.g. a width) that may be suitable forforming the at least one graphene layer 108 with a desired property. Forexample, in a case of a circularly cylindrical protrusion 106 with awidth 106W corresponding to a diameter d of the circularly cylindricalprotrusion 106, the diameter d of the protrusion may be chosen tofulfill the relation d=78.3×((n+m)²−n×m)^(0.5) pm for a combination ofinteger values of m and n that may not both be zero. The diameter ofthe, e.g. three-dimensionally shaped graphene layer 108, may correspondto the diameter d of the at least one protrusion 106. In a case wherem=n, the graphene layer 108 may form a carbon nanotube 108 c with anarmchair configuration. In a case where n is an integer and m is zero, acarbon nanotube 108 c with a zigzag configuration may be formed, and forother combinations of m and n, a carbon nanotube 108 c with a chiralconfiguration may be formed. An electrical conductivity of the carbonnanotube may vary with its diameter d. The electrical conductivity mayfor example vary between a metallic behavior and a semiconductingbehavior. For example, a band gap of the nanotube may vary from zero eV(corresponding to metallic behavior) up to a few eV, e.g. 2 eV(semiconducting behavior), depending on the diameter d and chirality.

In various embodiments, other properties (than the diameter) of the atleast one protrusion 106 may be adjusted, for example as describedabove, for obtaining a desired surface configuration of the peripheralouter surface 106 o of the at least one protrusion 106. The adjustmentof the properties may allow for the forming of the at least one graphenelayer 108 with specific properties. In various embodiments, arrangingthe crystal, e.g. the SiC substrate, to have a specific orientation mayallow for a forming of the at least one graphene layer 108, e.g. thecarbon nanotube 108 c, with a specific configuration (e.g., armchair,zigzag or chiral). In various embodiments, the shape of the at least oneprotrusion 106, e.g. may be adjusted for obtaining a desired property inthe at least one graphene layer 108 formed at or on the outer peripheralsurface of the at least one protrusion 106. For example, the peripheralouter surface 106 o of the at least one protrusion 106 may have apolygonal shape (e.g. a polygonal cross-section). In variousembodiments, an angle between two faces of the polygon having a commonedge (also referred to as the binding angle) may be varied. Thereby, avariation, e.g. a local variation, of the band gap of the at least onegraphene layer 108 formed on the outer peripheral surface 106 o of theat least one protrusion 106 may be possible. For example, decreasing thebinding angle may make the band gap (e.g. of the at least one graphenelayer 108) larger. The at least one graphene layer 108 may be asingle-walled or a multi-walled graphene layer 108.

In various embodiments, some or all of the above described parameters(e.g., termination (e.g. Si-face or C-face) of the surface of thecarbon-containing semiconductor material, e.g. of the substrate 102,epitaxy parameters, e.g. parameters of the annealing process, e.g.parameters used for the epitaxial formation of the graphene layer 108),and possibly other parameters, may be adjusted, for example as describedabove, for forming the at least one graphene layer 108 with the desiredproperties, e.g. single- or multiwall graphene layer, e.g. single- ormultiwall carbon nanotubes, specific band gaps, etc.

In various embodiments, as shown in FIG. 1D, the carbon-containingsemiconductor material of the at least one protrusion 106 may be removedfrom an inside 110 of the at least one graphene layer 108, e.g. from aninside 110 of the at least one graphene structure 108 s. In other words,the method of forming a graphene structure 108 s may further includeremoving a portion of the protrusion 106 that may reside within thegraphene layer 108, e.g. the graphene structure 108 s. In variousembodiments, the removing the portion of the protrusion may includeetching, for example using etching processes as described above for thestructuring of the semiconductor body 102. In an exemplary case wherethe graphene layer 108 may have been formed also on the top of theprotrusion 106, that top portion of the graphene layer 108 may beremoved before the removal of the carbon-containing semiconductormaterial from the inside 110 of the at least one graphene layer 108. Theremoving of the top portion of the graphene layer 108 may includechemical mechanical polishing and/or any other known means.

In various embodiments, portions of the at least one graphene layer 108may be removed from regions where the graphene layer 108 may not bedesired. As for example shown in FIG. 1E, a portion of the graphenelayer 108 formed on the first recessed surface 1021 r of thesemiconductor body 102 may be removed, for example by etching.

In various embodiments, as described above and shown in FIG. 1A to FIG.1E, a graphene structure 108 s may be formed. A graphene structurearrangement may include a semiconductor substrate 102, e.g. a base 102 bof the semiconductor substrate 102, and the graphene structure 108 s,e.g. at least one cylindrical graphene structure 108 s. A first end 108b of the cylindrical graphene structure 108 s may be attached to thesemiconductor substrate 102, e.g. to the base 102 b of the semiconductorsubstrate 102. An outside of the cylindrical graphene structure 108 smay be free from material of the semiconductor substrate 102.

In various embodiments, an inside of the cylindrical graphene structure108 s may be free from material, e.g. free from material of thesemiconductor substrate. Alternatively, an inside of the cylindricalgraphene structure 108 s may be filled with a semiconductor materialcontaining carbon. The semiconductor material filling the cylindricalgraphene structure 108 s may be the same as the semiconductor materialof the semiconductor substrate 102.

FIGS. 2A and 2B show two stages of a method of forming a graphenestructure according to various embodiments.

Various components, materials, processes, parameters etc. applying tovarious embodiments shown in FIG. 2A and FIG. 2B may be similar oridentical to those described above. Their description may not berepeated here.

In various embodiments, as shown in FIG. 2A, an opening 110 may beformed in the at least one protrusion 106 of the semiconductor body 102.Thereby, a hollow protrusion 106, e.g. a hollow cylinder 106, may beformed. The hollow protrusion 106 may have an outer peripheral surface106 o shaped according to any of the various embodiments describedabove. An inner peripheral surface 106 i of the hollow protrusion 106may have any shape. In various embodiments, the inner peripheral surface106 i may essentially trace the outer peripheral surface 106 o, therebyforming a hollow protrusion 106, e.g. a hollow cylinder 106, with anessentially uniform wall thickness.

In various embodiments, the forming of the graphene structure 108 s mayfurther include an annealing of the semiconductor body 102. During theannealing, the inner peripheral surface 106 i may, in addition to atleast the outer peripheral surface 106 o, be exposed. At least onegraphene layer 108 may thus be formed at least on the outer peripheralsurface 106 o and on the inner peripheral surface 106 i.

FIGS. 3A and 3B show graphene structures 108 s in accordance withvarious embodiments.

Processes described above may have been employed for forming the atleast one graphene layer 108, e.g. the at least one graphene structure108 s, shown in each of FIG. 3A and FIG. 3B.

Furthermore, the at least one graphene layer 108, e.g. the at least one,e.g. three-dimensional, graphene structure 108 s, may be removed fromthe semiconductor base 102 b of the semiconductor body 102. In otherwords, the method of forming a graphene structure may, in variousembodiments, further include detaching the at least one graphenestructure 108 s, and possibly also the at least one protrusion 106, froma remaining portion, e.g. the base 102 b, of the semiconductor body,thereby forming at least one detached cylindrical graphene structure,which may or may not be filled with the carbon-containing semiconductormaterial. In other words, at least one detached graphene layer 108, e.g.a plurality of detached graphene layers 108, e.g. of individual detachedgraphene layers 108, e.g. of detached graphene structures 108 s, e.g. ofindividual detached graphene structures 108 s, may be formed. Each ofthe individual detached graphene layers 108, e.g. of the individualdetached graphene structures 108 s, may include a graphene monolayer ora graphene multilayer. The plurality of graphene layers/structures 108,108 s may essentially all have the same length. An inside of the atleast one graphene layer/structure 108, 108 s may be free or partiallyfree from the carbon-containing semiconductor material. Alternatively,the at least one graphene layer/structure 108, 108 s may be filled, e.g.completely or essentially completely, with the carbon-containingsemiconductor material, e.g. the carbon-containing semiconductormaterial that was used for forming the at least one graphene layer 108.

In an exemplary case where the individual graphene layer/structure 108,108 s includes a graphene multilayer, the individual graphenelayer/structure 108, 108 s may include a plurality of graphene layersthat may be arranged concentrically, i.e. one graphene layer/structureinside another graphene layer/structure.

In various embodiments, the at least one graphene layer/structure 108,108 s may include at least one carbon nanotube 108 c, for example asdescribed above.

In various embodiments, the at least one graphene layer/structure 108,108 s may include at least one carbon nanotube 108 c that may be filledwith carbon-containing semiconductor material, e.g. SiC, for example asdescribed above. A carbon nanotube in accordance with variousembodiments may be filled with silicon carbide.

In various embodiments, the at least one graphene layer/structure 108,108 s, e.g. the at least one carbon nanotube 108 c, may be removed fromthe semiconductor base 102 b of the semiconductor body 102 by etching.In the exemplary embodiment shown in FIG. 3A, with an inside of the atleast one graphene layer/structure 108, 108 s being free from thecarbon-containing semiconductor material, a removal of thecarbon-containing semiconductor material may for example be carried outas described in context with FIG. 1D for removing the carbon-containingsemiconductor material from an inside of the at least one graphene layer108 on a semiconductor body 102 with a graphene layer 108 formed on aperipheral outer surface 106 o of at least one protrusion 106 of thesemiconductor body 102 as for example shown in FIG. 1E. The etching maybe continued until the carbon-containing semiconductor material is notonly removed from the inside of the graphene structure 108 s, but alsofails to provide a connection to the base 102 b of the semiconductorbody 102, thereby releasing the at least one graphene layer/structure108, 108 s. An outer surface of the carbon nanotube may be uncovered.View 300A of FIG. 3A shows a cross section along the line A-A′ of FIG.3A for an example of an unfilled circularly cylindrical graphenelayer/structure/carbon nanotube 108, 108 s, 108 c, hence the graphenelayer/structure/carbon nanotube 108, 108 s, 108 c is shown as anunfilled circle.

In the exemplary embodiment shown in FIG. 3B, with an inside of the atleast one graphene layer/structure 108 being filled with thecarbon-containing semiconductor material, a removal of thecarbon-containing semiconductor material may for example be executed byannealing the semiconductor body 102 in a hydrogen atmosphere. In otherwords, the at least one graphene layer/structure 108, 108 s filled withthe carbon-containing semiconductor material, e.g. a carbon nanotube 108c filled with the carbon-containing semiconductor material, e.g. withsilicon carbide, may be decoupled from the semiconductor body 102, e.g.from a silicon carbide substrate, by annealing in a hydrogen atmosphere.An outer surface of the carbon nanotube may be uncovered. View 300B ofFIG. 3B shows a cross section along the line B-B′ of FIG. 3B for anexample of a filled circularly cylindrical graphenelayer/structure/carbon nanotube 108, 108 s, 108 c, hence the graphenelayer/structure/carbon nanotube 108, 108 s, 108 c is shown as a circlefilled with the carbon-containing semiconductor material of the at leastone protrusion 106.

FIGS. 4A to 4F show various stages of a method of forming a transistorin accordance with various embodiments.

In various embodiments, at least one graphene layer 108, e.g. a graphenelayer 108 according to an embodiment described above, may form part of atransistor, e.g. of a field effect transistor, e.g. a vertical fieldeffect transistor. The method of forming a graphene structure 108 s,e.g. a carbon nanotube, as described above may make a defined forming ofa field effect transistor with a vertical architecture possible.

A method of forming a transistor may include forming a graphenestructure 108 s, for example as described above.

The method of forming a transistor may, in various embodiments, includeforming a semiconductor body 102 including at least one protrusion 106including carbon-containing semiconductor material, and forming agraphene layer 108 at an outer peripheral surface of the at least oneprotrusion 106. The method of forming a transistor may, in variousembodiments, include forming at least one protrusion 106 with acylindrical, e.g. outer peripheral, surface, the protrusion 106projecting from a first side 1021 of a semiconductor body 102, whereinthe at least one protrusion 106 may be formed from a carbon-containingsemiconductor material, and thereafter annealing the semiconductor body102 such that graphene may form on the at least one cylindrical surface,thereby forming at least one cylindrical graphene structure 108 s.

In FIG. 4A, the transistor is shown at an intermediate stage after theforming of the graphene layer 108. The transistor at this intermediatestage may differ from the configuration of FIG. 1C in that the graphenelayer 108 in FIG. 4A may not be formed at or may have been removed froma top of the at least one protrusion 106 and from the first recessedsurface 1021 r of the semiconductor body 102. The removal of portions ofthe graphene layer from the first recessed surface 1021 r, which maylead to the graphene layers 108 formed on, e.g. a plurality of, the atleast one protrusion 106 being electrically insulated from each other(or at least, not being electrically connected), e.g. by etching, mayfor example be carried out by a spacer etching process (which moregenerally may refer to an etching process that creates a spacer at aside wall of some other element). View 400A shows a cross section alongline A-A′ of FIG. 4A.

As shown in FIG. 4B, the method of forming a transistor may, in variousembodiments, further include forming a dielectric layer 440 on anoutside of the at least one graphene layer/structure 108, 108 s, e.g. onan outside of a cylindrical graphene layer/structure 108, 108 s. Thedielectric layer 440 may further be formed on the first recessed surface1021 r and/or on a top of the at least one protrusion 106. Thedielectric layer 440 may be formed using known techniques and materialsfor forming a gate dielectric, for example atomic layer deposition orthe like, for example for depositing an oxide. View 400B shows a crosssection along line B-B′ of FIG. 4B.

As shown in FIG. 4C, the method of forming a transistor may, in variousembodiments, further include forming a gate 442 around an outside of thegate dielectric 440 formed around the at least one graphene layer 108,e.g. the cylindrical graphene structure 108 s. The gate 442 may beelectrically insulated from the at least one graphene layer 108, e.g.the cylindrical graphene structure 108 s. The electrical insulation maybe provided by the gate dielectric 440. The forming the gate 442 mayinclude depositing an electrically conductive material, e.g.polysilicon, a metal or metal alloy, or any other suitable electricallyconductive material, at least around an outside of the gate dielectric440. In various embodiments, the material for forming the gate 442 maybe deposited on the first side of the semiconductor body 102, e.g. abovethe first recessed surface 1021 r of the semiconductor body 102. Thematerial for forming the gate 442 may be deposited as a layer. The gate442 (which may include a plurality of gates 442, e.g. one gate for eachof a plurality of graphene layers/structures 108, as shown in FIG. 4C)may be formed by etching those portions of the layer that may not formpart of the gate 442. As for example shown in FIG. 4C, the gate 442 mayhave a shape of a cone-shaped annulus around the at least one graphenelayer/structure 108, 108 s. The etching of the gate 442 may for examplebe carried out by a spacer etch process.

An intermediate structure of the transistor formed by the processes upto now may be an essentially free-standing structure, as shown in FIG.4C. View 400C shows a cross section along line C-C′ of FIG. 4C.

As shown in FIG. 4D, the, e.g. free-standing, structure may bestabilized by forming a stabilizer 444 around the structure, therebymechanically stabilizing the structure. The stabilizer 444 may forexample include or be a dielectric material or layer. The stabilizer 444may for example be formed by chemical vapor deposition. The forming ofthe stabilizer 444 may enable conducting a subsequent process. Using forexample a chemical mechanical polishing process, a portion of the gatedielectric 440 that may have been formed on a top of the at least oneprotrusion 106 may be removed. Thereby, access may be provided to thecarbon-containing semiconductor material within the at least onegraphene layer/structure 108, as shown in FIG. 4D.

As shown in FIG. 4E, the carbon-containing semiconductor material, e.g.the silicon carbide, e.g. a silicon carbide core, may be removed fromwithin the at least one graphene layer/structure 108, 108 s, for exampleby etching, for example as described above.

As shown in FIG. 4F, at least one electrode 446, e.g. including orconsisting of an electrically conductive material, may be formed, e.g.by known means, e.g. by deposition and etching, on the at least onegraphene layer/structure 108, 108 s, e.g. on a top surface at the topend 108 t of the at least one graphene layer/structure 108, 108 s, andpossibly on the gate dielectric 440 and/or the stabilizer 444. The atleast one electrode 446 may be electrically conductively connected tothe at least one graphene layer/structure 108, 108 s. The at least oneelectrode 446 may provide one of a source/drain contact of thetransistor, and another source/drain contact of the transistor may beprovided electrically contacting a bottom end 108 b of the at least onegraphene layer/structure 108, 108 s, e.g. by an electrically conductivestructure formed in the semiconductor body 102, e.g. the base 102 b ofthe semiconductor body 102 (not shown). For example, the at least oneelectrode 446 may form the drain contact. In other words, the method offorming the transistor may further include electrically connecting thetop end 108 t of the at least one, e.g. cylindrical, graphenelayer/structure 108, 108 s to a first source/drain contact 446, andelectrically connecting a bottom end 108 b of the, e.g. cylindrical,graphene layer/structure 108, 108 s to a second source/drain contact.

In various embodiments, vias, buried structures (not shown) or the likemay be used for electrically contacting the gate 442.

FIGS. 5A to 5C show various stages of a method of forming a graphenestructure 108 s (including portions 108 a and 108 b) in accordance withvarious embodiments.

Various components, materials, processes, parameters etc. applying tovarious embodiments shown in FIG. 5A to FIG. 5C may be similar oridentical to those described above. Their description may not berepeated here.

As shown in FIG. 5A, the at least one protrusion 106 of thesemiconductor body 102 may, in various embodiments, include dopedregions, e.g. two doped regions 106 a and 106 b. In various otherembodiments, the at least one protrusion 106 may include fewer or moredoped regions. A first doped region 106 a may be of a first conductivitytype. A second doped region 106 b may be of a second conductivity type.The first conductivity type may be an n-type conductivity type, and thesecond conductivity type may be a p-type conductivity type, as shown inFIG. 5A, or vice versa (not shown). An n-doping of the carbon-containingsemiconductor material, e.g. silicon carbide, may for example beachieved by doping with group V atoms, e.g. arsenic or phosphorus. Ap-doping of the carbon-containing semiconductor material, e.g. siliconcarbide, may for example be achieved by doping with group III atoms,e.g. indium, gallium or aluminum.

In various embodiments, the first doped region 106 a and the seconddoped region 106 b may, as shown in FIG. 5A, be arranged vertically(e.g. stacked) in the at least one protrusion 106. Other arrangements ofthe doped regions 106 a, 106 b with the different conductivity types maybe chosen, e.g. the first doped region 106 a and the second doped region106 b may be arranged in different azimuthal directions of the at leastone protrusion 106.

The method of forming a graphene structure may be carried out forexample as described in an embodiment described above. This may, invarious embodiments, result in at least one graphene layer 108 that mayinclude a first doped region 108 a of a first conductivity type and asecond doped region 108 b of a second conductivity type. The first dopedregion 108 a of the at least one graphene layer 108 may form in a regionwhere the at least one graphene layer 108 may be formed from thecarbon-containing semiconductor material with the doping of the firstconductivity type. The second doped region 108 b of the at least onegraphene layer 108 may form in a region where the at least one graphenelayer 108 may be formed from the carbon-containing semiconductormaterial with the doping of the second conductivity type. In otherwords, a doping of the different doping regions 106 a, 106 b may betransferred to the at least one graphene layer 108, e.g. during theannealing of the semiconductor body 102. Thereby, a graphene structure108 s with doped regions 108 a, 108 b may be formed. For example, acarbon nanotube with doped regions 108 a, 108 b may be formed, i.e. adoped carbon nanotube.

In various embodiments, a pn-junction may be formed in the at least onegraphene layer/structure 108, 108 s. For example, a carbon nanotube witha pn-junction may be formed.

In various embodiments, as shown in FIG. 5C, the carbon-containingsemiconductor material may be removed from inside the at least one dopedgraphene layer/structure 108, 108 s, as described above. A semiconductorbody 102, e.g. a base 102 b of the semiconductor body 102, with at leastone unfilled doped graphene layer/structure 108, 108 s may thus beformed.

In various embodiments, the at least one unfilled doped graphenelayer/structure 108, 108 s may be detached from the base 102 b of thesemiconductor body 102 as described above.

In various embodiments, the at least one doped graphene layer/structure108, 108 s filled with the doped carbon-containing semiconductormaterial may be detached from the base 102 b of the semiconductor body102 as described above.

FIGS. 6A and 6B show various stages of a method of forming a graphenestructure in accordance with various embodiments.

Various components, materials, processes, parameters etc. applying tovarious embodiments shown in FIGS. 6A and 6B may be similar or identicalto those described above. Their description may not be repeated here.

As shown in FIG. 6A, an opening 660 may be formed in a body 102, e.g. ina semiconductor body, e.g. in a body containing carbon. The opening 660may for example be etched, e.g. in a similar process as described abovefor forming the at least one protrusion. A graphene layer 108 may beformed on an inner peripheral surface of the opening 660 formed in thebody 102, for example as described above for forming the graphene layer108 on the outer peripheral surface 106 o of the at least one protrusion106.

As shown in FIG. 6B, in various embodiments, a portion of the body 102outside the graphene layer 108 (which may form a closed surface) may beremoved, for example by etching etc. as described above.

In various embodiments, the graphene layer 108 may be formed on theinner peripheral surface of the opening 660 formed in the body 102 withsuch a specific diameter 660D that a carbon nanotube 108 c may form. Inother words, the diameter 660D of the opening 660 may fulfill a specificrelation. For example, the diameter 660D may be chosen to fulfill therelation d=78.3×((n+m)²−n×m)^(0.5) pm for a combination of integervalues of m and n that may not both be zero.

In various embodiments, the graphene layer 108, e.g. the carbon nanotube108 c, may remain connected to a base 102 b of the body 102, e.g. of thesemiconductor body. Alternatively, the graphene layer 108, e.g. thecarbon nanotube 108 c, may be removed from the base 102 b of the body102, e.g. of the semiconductor body. Thereby, an unfilled carbonnanotube 108 c, e.g. as shown in FIG. 3A, may be formed.

FIG. 7 shows a schematic diagram 700 of a method of forming a graphenestructure in accordance with various embodiments.

As shown in FIG. 7, the method of forming a graphene structure mayinclude forming a semiconductor body including at least one protrusionincluding carbon-containing semiconductor material (in 710).

The method may further include forming a graphene layer at an outerperipheral surface of the at least one protrusion (in 720).

FIG. 8 shows a schematic diagram 800 of a method of forming a graphenestructure in accordance with various embodiments.

As shown in FIG. 8, the method of forming a graphene structure mayinclude forming at least one structure with at least one cylindricalouter surface from a silicon carbide substrate, the structure projectingfrom at least one side of the silicon carbide substrate (in 810).

The method may further include annealing the silicon carbide substratesuch that graphene forms on at the at least one cylindrical outersurface, thereby forming at least one cylindrical graphene structure (in820).

FIG. 9 shows a schematic diagram 900 of a method of forming a graphenestructure in accordance with various embodiments.

As shown in FIG. 9, the method of forming a graphene structure mayinclude forming a plurality of pillars including silicon carbide (in910).

The method may further include forming a plurality of carbon nanotubesfrom the plurality of pillars by thermal decomposition of the siliconcarbide at an outer peripheral surface of the plurality of pillars (in920).

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming a body including at least oneprotrusion; and forming a graphene layer at an outer peripheral surfaceof the at least one protrusion. In various embodiments, the body may bea semiconductor body. In various embodiments, the at least oneprotrusion may include carbon-containing semiconductor material.

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming a semiconductor body includingat least one protrusion including carbon-containing semiconductormaterial, and forming a graphene layer at an outer peripheral surface ofthe at least one protrusion. In various embodiments, thecarbon-containing semiconductor material may be silicon carbide. Invarious embodiments, the forming of the graphene layer may includeforming, by thermal decomposition of the silicon carbide, the graphenelayer around the outer peripheral surface of the at least one protrusionfrom the silicon carbide of the at least one protrusion. In variousembodiments, the semiconductor body may include a semiconductorsubstrate, wherein forming the at least one protrusion may includeforming at least one trench in the semiconductor substrate. In variousembodiments, the semiconductor body may include a semiconductorsubstrate, wherein forming the at least one protrusion may includeepitaxially growing the at least one protrusion on the semiconductorsubstrate. In various embodiments, the graphene layer at an outerperipheral surface of the at least one protrusion forms a closedsurface. In various embodiments, the method may further include removinga portion of the protrusion that resides within the graphene layer. Invarious embodiments, the removing the portion of the protrusion mayinclude etching. In various embodiments, the method may further includeforming an opening in the at least one protrusion, and forming agraphene layer on a surface of the opening. In various embodiments, thegraphene layer may include at least one carbon nanotube. In variousembodiments, the forming of the graphene layer may include annealing ofthe semiconductor body. In various embodiments, one or more processparameters of the annealing may be adjusted such that the at least onecarbon nanotube is configured as a single-walled carbon nanotube. Invarious embodiments, one or more process parameters of the annealing maybe adjusted such that the at least one carbon nanotube is configured asa multi-walled carbon nanotube. In various embodiments, the processparameters of the annealing may include at least one of an annealingtemperature, an annealing duration, an atmospheric pressure, andconstituents of the atmosphere. In various embodiments at least one of awidth of the protrusion, a shape of the protrusion, a crystalorientation of the semiconductor body, and a surface termination of theprotrusion may be selected or adjusted such that the at least one carbonnanotube is a single-walled carbon nanotube or a multi-walled carbonnanotube. In various embodiments, the annealing temperature may be in arange from about 1150° C. to about 1800° C. In various embodiments, theannealing duration may be in a range from about 5 minutes to about 60minutes. In various embodiments, the carbon-containing semiconductormaterial may be silicon carbide, and the surface termination of the atleast one semiconductor structure may be silicon. In variousembodiments, the at least one protrusion may include a first dopedregion having a first conductivity type, and a second doped regionhaving a second conductivity type. In various embodiments, a diameter dof the protrusion may be chosen to fulfill the relationd=78.3×((n+m)²−n×m)^(0.5) pm, wherein n and m may be integer values, atleast one of n and m being greater than 0. In various embodiments, n=m,n≠0, m≠0. In various embodiments, m=0, n≠0. In various embodiments, n≠m,m≠0, n≠0. In various embodiments, the method may further includedetaching the at least one protrusion from a remaining portion of thesemiconductor body after the forming of the graphene layer. In variousembodiments, the method may further include detaching the at least onegraphene layer from a remaining portion of the semiconductor body. Invarious embodiments, the at least one detached graphene layer mayinclude a plurality of graphene layers of essentially equal length. Invarious embodiments, the outer peripheral surface of the at least oneprotrusion may be cylindrical. In various embodiments, the outerperipheral surface of the at least one protrusion may be circularlycylindrical or polygonal. In various embodiments, at least one physicalproperty of the graphene layer may vary in an azimuthal direction of theprotrusion.

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming at least one structure with atleast one cylindrical outer surface from a silicon carbide substrate,the structure projecting from at least one side of the silicon carbidesubstrate; and annealing the silicon carbide substrate such thatgraphene forms at the at least one cylindrical outer surface, therebyforming at least one cylindrical graphene structure.

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming a plurality of pillarscontaining silicon carbide, and forming a plurality of carbon nanotubesfrom the plurality of pillars by thermal decomposition of the siliconcarbide at an outer peripheral surface of the plurality of pillars.

In various embodiments, a carbon nanotube arrangement is provided. Thecarbon nanotube arrangement may include a plurality of carbon nanotubesdisposed over a silicon carbide substrate, wherein an outer surface ofthe carbon nanotubes is uncovered. In various embodiments, the carbonnanotubes may be filled with silicon carbide.

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming at least one opening in a body;forming a graphene layer at an inner peripheral surface of the at leastone opening; and at least partially removing the body from an outerperipheral surface of the graphene layer. In various embodiments, thebody may include or may be made from silicon carbide. In variousembodiments, the opening may be cylindrical.

In various embodiments, a method of forming a graphene structure isprovided. The method may include forming at least one cylindricalopening in a body, wherein a diameter of the opening may be chosen tofulfill the relation d=78.3×((n+m)²−n×m)^(0.5) pm, wherein n and m areinteger values, at least one of n and m being greater than 0; andforming a graphene layer at an inner peripheral surface of the at leastone opening. In various embodiments, the body may include or may be madefrom silicon carbide.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims. The scope of the invention is thusindicated by the appended claims and all changes which come within themeaning and range of equivalency of the claims are therefore intended tobe embraced.

What is claimed is:
 1. A method of forming a graphene structure,comprising: forming at least one opening in a body; and forming agraphene layer at an inner peripheral surface of the at least oneopening.
 2. The method of claim 1, further comprising at least partiallyremoving the body from an outer peripheral surface of the graphenelayer.
 3. The method of claim 1, wherein the body comprises siliconcarbide.
 4. The method of claim 3, wherein forming the graphene layer atthe inner peripheral surface of the at least one opening comprisesannealing the body so that the graphene layer forms at an innerperipheral surface of the at least one opening.
 5. The method of claim4, wherein process parameters of the annealing comprise at least one ofan annealing temperature, an annealing duration, an atmosphericpressure, and constituents of the atmosphere.
 6. The method of claim 4,wherein an annealing temperature is in a range from about 1150° C. toabout 1800° C.
 7. The method of claim 4, wherein an annealing durationis in a range from about 5 minutes to about 60 minutes.
 8. The method ofclaim 1, wherein the graphene layer is a closed surface.
 9. The methodof claim 1, wherein the graphene layer is a carbon nanotube.
 10. Themethod of claim 9, wherein the carbon nanotube is unfilled.
 11. Themethod of claim 2, wherein at least partially removing the body from anouter peripheral surface of the graphene layer comprises etching thebody.
 12. The method of claim 1, comprising removing the graphene layerfrom the body.
 13. A method of forming a graphene structure, comprising:forming at least one cylindrical opening in a body, wherein a diameterof the opening is chosen to fulfill a relation d=78.3□((n+m)2−n×m)0.5pm, wherein n and m are integer values, at least one of n and m beinggreater than 0; and forming a graphene layer at an inner peripheralsurface of the at least one opening.
 14. The method of claim 13, furthercomprising at least partially removing the body from an outer peripheralsurface of the graphene layer.
 15. The method of claim 14, wherein atleast partially removing the body from an outer peripheral surface ofthe graphene layer comprises etching the body.
 16. The method of claim13, wherein the body comprises silicon carbide.
 17. The method of claim16, wherein forming the graphene layer at the inner peripheral surfaceof the at least one opening comprises annealing the body so that thegraphene layer forms at an inner peripheral surface of the at least oneopening.
 18. The method of claim 13, wherein the graphene layer is acarbon nanotube.